3.1 Barletta sinkhole

In the night between 2 and 3 May 2010, a large sinkhole occurred in the rural area of San Procopio (De Giovanni et al., 2011; Parise et al., 2013), near the town of Barletta (Apulia, southern Italy); the maximum diameter of the depression has been calculated to be approximately equal to 32 m at the ground surface (Fig. 5).

Figure 5Aerial view of the sinkhole that occurred in the Barletta area.

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Later on, geological and speleological surveys have revealed the existence of a complex network of artificial tunnels excavated presumably between the 19th and 20th century in order to extract calcarenite rocks as a building material (De Giovanni et al., 2011; Parise et al., 2013). These studies have revealed that the underground cavity was formed of wide and long tunnels with a large number of isolated pillars showing an irregular spatial distribution, as reported in Fig. 6a. In the sinkhole area (N–W sector of the cavity), the spatial distribution of pillars was coarser as compared with the rest of the cavity system, and it was characterized by the presence of only eight pillars located at a distance of about 10–12 m from the others; as such, these pillars were deemed to be heavily overloaded and probably subjected to high stress conditions.

Figure 6(a) Schematic map of the Barletta underground calcarenite quarry (adapted from Luisi et al., 2015; the area involved in the collapse is shown in orange, pillars are in dark gray, and tunnels and excavated zones are in light gray); (b) original stratigraphy of the cavity (before collapse).

In order to detect the causes that led to the collapse of the underground quarry, it should be noted that instability evidence, such as signs of pillar crushing or fractures with detachments from the vault and the walls (Fig. 7), was found throughout the cavity, especially close to the sinkhole area (De Giovanni et al., 2011). Therefore, starting from the original geometrical configuration of the cavity shown in Fig. 6b, the loss of strength produced by the failure of the inner pillars, where high stress conditions are likely, may have generated an increase in the loading conditions for the whole roof, with the consequent generation of a sinkhole mechanism.

Figure 7Instability evidence at the Barletta underground quarry: (a) tensile fracturing of the vault; (b) block detachment from the vault; (c) open fractures on pillars, and vault collapses in the area closest to the sinkhole; (d) crushing of pillar with joints (adapted from De Giovanni et al., 2011).

In order to verify the stability conditions using the charts proposed by Perrotti et al. (2018), an initial value of the cavity width of about 10–12 m, corresponding to the largest distance between two adjacent pillars (see Fig. 6), has been assumed, bearing in mind that the failure of the nearby pillars has presumably implied an increase in the effective L parameter. Speleological surveys have indicated an average thickness of the calcarenite deposits in the study area of about 6 m, with a minimum value of 4 m (De Giovanni et al., 2011) and with an upper layer of about 0.5–0.8 m composed of sandy–silty topsoil (unit weight γ=20 kN m⁻³) overlying a 5.2–5.5 m thick calcarenite layer (γ=17 kN m⁻³). In the sinkhole area, the height of the cavity rooms has been generally measured to be about 5 m.

Uniaxial compression tests performed in the laboratory on calcarenite samples taken in the sinkhole area have indicated values of uniaxial compressive strength of about 1–2 MPa under dry conditions and about 0.75–1 MPa under saturated conditions (Luisi et al., 2015); tensile strength values derived from indirect tension tests have instead resulted to be approximately equal to 0.1–0.2 MPa. Consequently, the parameter m_i to be used in the Hoek–Brown failure criterion results in a range between 6 and 11.

Hence, based on these evaluations, the nondimensional ratios L∕t and L∕h can be estimated in the following ranges: $\mathrm{1.81}<L/t<\mathrm{2.31}$ and $\mathrm{2}<L/h<\mathrm{2.4}$.

The vertical stress at a depth of h=6 m is estimated to be equal to

and, assuming σ_c=1 MPa, a ratio σ_c∕σ_v equal to about 9.6 is obtained.

In Table 2 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Barletta underground quarry are shown.

Table 2Geometrical and mechanical parameters and adopted values for stability chart application to the Barletta underground quarry.

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Therefore, considering the chart corresponding to a value m_i=8 (Fig. 3), and specifically the curve corresponding to L∕h ratio between 2 and 3, in the initial conditions (pillars that have not failed), the cavity is found to be in the stability zone (Fig. 8); however, if a strength loss of the nearby pillars is accounted for, an increase in the L representative parameter leads to a gradual increase in the ratio L∕t (as well as of L∕h ratio), with the consequent decrease in the safety margin until reaching the threshold curve corresponding to the L∕h value (Fig. 8), thus indicating failure conditions.

Figure 8Application of stability chart (m_i=8) for the Barletta case study.

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Figure 8 also shows that the cavity is close to failure conditions already for values of ratio L∕t larger than 2.75; therefore, even with the loss of the strength provided by a single pillar, a ratio L∕t corresponding to the achievement of the threshold stability conditions follows.

3.2 Marsala sinkhole

A sinkhole took place in the town of Marsala (Sicily, Italy) in June 2011 in the area where underground quarries were excavated according to the room-and-pillar technique at depths ranging from 3–4 m to about 15 m; after the quarry abandonment, since the 1960s, the cavity has been progressively subjected to instability phenomena, represented by deformations and block detachments from the vaults and the pillars.

A detailed map of the underground cavity luckily existed before the collapse, thanks to a speleological survey carried out in 2000 (Vattano et al., 2013). This allowed us to properly map the sinkhole boundary above the underground quarry; with a minimum diameter of about 25–30 m at the ground level, the sinkhole is shown in Fig. 9. The figure shows that the examined quarry consists of rooms with a quadrangular shape, in most cases connected and/or separated by thin rock walls or pillars. As specifically concerns the sinkhole area, the excavation was carried out according to an irregular scheme, leaving very small pillars and slight internal walls; larger sizes of the internal supporting elements, as well as lower room spans, are instead observed in the rest of the cavity system. The average room height has been estimated to be equal to 2.7 m, with the roof thickness varying from 8.2 to 11.8 m.

Figure 9Plan of the Marsala underground quarry, with indication of the sinkhole area (adapted from Vattano et al., 2013).

Figure 10Instability evidence at the Marsala underground quarry: (a) fracturing of a pillar; (b) bending and failure of a pillar; (c) material detachments from the vault; (d, e) diffuse fracturing within the walls and the vaults (Bonamini et al., 2013).

For this study, Fazio et al. (2017) have proposed a three-dimensional finite-element back analysis and have found that the weakness of these overstressed internal structural elements could have been the reason for initial local failure and then for global failure. In particular, the collapse of the pillars and the internal walls (very thin along the A-A section of Fig. 9) could have progressively entailed an increase in the width of the open galleries, leading to a total length, L, approximately equal to that of the sinkhole (D≈25–30 m, Fig. 9). Local failures of pillars and thin walls, as well as detachments and fracturing processes of the vault, are widely diffuse within the Marsala cavity, as documented in Fig. 10 (Bonamini et al., 2013).

Figure 11Stratigraphy of Marsala underground quarry traced along the A-A section.

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The calcarenites outcropping in the study area can be schematized according to two lithotypes, with a top layer (thickness in a range between 8.2 and 11.8 m) characterized by poor mechanical properties and a stiffer deeper layer (Fazio et al., 2017); in Fig. 11 the stratigraphy traced along the A-A section of Fig. 9 is reported.

For the upper softer lithotype the dry unit weight is measured in the range between 12 and 15 kN m⁻³, whereas the same parameter under saturated conditions is between 13.5 and 17 kN m⁻³. Uniaxial compressive strength under saturated conditions has been measured to reach about σ_c=1.3–1.6 MPa, whereas with a saturation degree equal to zero σ_c=2–3 MPa. The value of the tensile strength can be assumed to be 1∕8–1∕10 of the compressive strength, in accordance with experimental works on similar calcarenite rocks (Andriani and Walsh, 2010; Ciantia et al., 2015), so the m_i parameter to be used in the Hoek–Brown strength criterion is in a range between 8 and 10.

Table 3Geometrical and mechanical parameters and adopted values for stability chart application to the Marsala underground quarry.

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Based on the aforementioned parameters, considering a cavity width L≈25–30 m (corresponding to the collapse of internal pillars and walls in Fig. 9); an average height, h, of 2.7 m; and an average overburden thickness, t, of 10 m, the corresponding nondimensional ratios L∕t and L∕h are in the following ranges: $\mathrm{2.5}<L/t<\mathrm{3}$ and $\mathrm{9.2}<L/h<\mathrm{11.1}$.

If a unit weight value γ_calc of 16 kN m⁻³ is assumed, the vertical stress at a depth of t=10 m is equal to ${\mathit{\sigma }}_{\mathrm{v}}\approx ({\mathit{\gamma }}_{\mathrm{calc}}\cdot t_{\mathrm{calc}})=\mathrm{160}$ kPa. Finally, assuming σ_c=2 MPa (corresponding to an intermediate value between saturated and dry conditions), a ratio σ_c∕σ_v approximately equal to 12.5 is obtained.

In Table 3 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Marsala underground quarry are shown.

Figure 12 shows the representative state of the Marsala cavity stability in the stability chart corresponding to m_i=8. The figure indicates that the state is located on the curve characterized by $L/h>\mathrm{3}$, and this confirms the unstable condition of the underground quarry.

Figure 12Application of stability chart (m_i=8) for the Marsala underground quarry.

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3.3 Gallipoli sinkhole

In the eastern urban area of the town of Gallipoli (southern Apulia) a large sinkhole occurred in 2007, between 29 March and 1 April, with the opening of a subelliptical 12 m × 18 m chasm (Fig. 13a), followed by a significant widening of the subsidence area at the ground level (Fig. 13b) which affected some buildings located nearby.

Figure 13Pictures of the 2007 Gallipoli sinkhole: (a) the first sinkhole as appeared in 29 March; (b) enlargement of the chasm on 1 April.

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Geological surveys performed soon after the collapse detected the existence of a complex underground cavity net on a single level; although a room-and-pillar excavation technique was adopted, the resulting geometry of the cavity system is highly irregular, with rooms located at variable depth from the ground level: in particular, in the area where the sinkhole occurred, the depth of the cave bottom is about 8 m, with a roof thickness of less than 3–4 m. Moreover, diffuse signs of local instability, such as block detachments from the vault and the lateral walls, debris heaps on the floor and fractures of pillars due to crushing were found within the cavity rooms (Delle Rose, 2007; Parise, 2012). Some of these local instabilities are shown in Fig. 14.

Figure 14Evidence of instability at the Gallipoli underground quarry: (a) extensive fracturing in a pillar; (b) view of sinkhole from the bottom; (c) inner view of one of the longest rooms in the cavity (block detachments from the vault and debris heaps on the floor); (d) incipient block detachment from a pillar.

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Based on the investigations performed, a reconstruction of the cavity geometry, before the collapse, was carried out. Figure 15 shows the position of the remaining pillars, the zones with the accumulation of debris or detachments of blocks, and the detailed perimeter of the sinkhole for both the first collapse and the subsequent enlargement. The buildings and the roads on the ground surface overlying the area are also shown in the map.

Figure 15Map of the underground quarry in Via Firenze, Gallipoli, and overlying built environment.

In the sinkhole area, deposits of the Salento calcarenites, consisting of alternations of calcarenite rocks and looser sediments, crop out; the rock volumes affected by the mining activity (i.e., the calcarenite) appear to be massive, whereas the upper layer, forming the cavity roof, is formed of laminated and stratified calcarenite deposits with very low mechanical properties (Delle Rose, 2007; Parise, 2012). Based on the saturation degree, uniaxial compressive strength σ_c results in a range between 2.5 and 3 MPa for dry samples and 1.7–2.3 MPa for saturated rock (Ciantia et al., 2015). Tensile strength is variable between 0.7 and 1 MPa both in dry and saturated conditions, so a parameter m_i=3–4 of the Hoek–Brown failure criterion has been derived accordingly. A unit weight about equal to 17.5 kN m⁻³ has also been assumed.

As concerns the application of the stability charts to the Gallipoli case study, a cave width L of about 18 m (Fig. 15) between two adjacent pillars is considered. The section trace along L is reported in Fig. 16; the overburden thickness is assumed to be t=3–4 m, and the height of the cavity is h=4–5 m, so the nondimensional ratios L∕t and L∕h are in the following ranges: $\mathrm{4.5}<L/t<\mathrm{6}$ and $\mathrm{3.6}<L/h<\mathrm{4.5}$.

Figure 16Cross section of the failed cavity in Gallipoli.

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The cavity roof is composed almost entirely by the upper calcarenite layers with lower mechanical properties, so a value of σ_c=2.7 MPa can be assumed. The vertical stress at the depth of h=3–4 m is

and, consequently, the ratio σ_c∕σ_v is in the range 38.6–51.3.

In Table 4 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Gallipoli underground quarry are shown.

Table 4Geometrical and mechanical parameters and adopted values for stability chart application to the Gallipoli underground quarry.

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Taking into account the stability charts corresponding to m_i=3 and, specifically, the threshold curve for $L/h>\mathrm{3}$, the representative area of the investigated cavity is very close to the threshold curve (Fig. 17); therefore, it results that the cavity was in a state of incipient failure, so some external factor, for example vibrations or concentrated seepages, could have triggered the instability.

Figure 17Application of stability chart (m_i=3) for the Gallipoli underground quarry.

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3.4 Cutrofiano underground caves

In the last century several underground quarries were excavated at the outskirts of the town of Cutrofiano (southern Apulia) with the room-and-pillar technique. Later on, these quarries were abandoned, and the urban area expanded above the areas originally distinguished by the presence of cavities. Geological surveys have highlighted, in the southern part of the town, the existence of a diffuse net of underground cavities. The location of three quarries, respectively named Cave A, Cave B and Cave C, with respect to the overlying built-up environment, is reported in Fig. 18.

Figure 18Location of the examined underground quarries at Cutrofiano.

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All the three quarries give evidence of signs of local instability, such as detachments of material from the walls and the vaults or pillar crushing that, frequently, represent prodromal signals of a possible general failure (Parise and Lollino, 2011). Figure 19 highlights some of the typical local failures detected in the Cutrofiano underground quarries.

Figure 19Signs of local instability in the Cutrofiano underground quarries: (a) diffuse fracturing of a wall; (b) detachments of material from walls; (c) massive falls from the walls, with heavy production of debris heaps on the floor; (d) open fractures at the pillar rim, in relation to the main shaft of access to the cavity.

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For each of the examined cavities, a detailed geometrical and geological survey has been performed. The geological setup of the area is formed of shallow layers of clays, silts and/or sands that overlie a stiffer layer of calcarenite, locally named “Mazzaro”, which generally represent the roof of the quarries. Therefore, in order to apply the stability charts the Mazzaro level has been considered.

Figure 20Plan and stratigraphy of the underground cavity A (adapted from Maglio and Ligori, 2014).

Figure 21Plan and stratigraphy of the underground cavity B (adapted from Maglio and Ligori, 2014)

From a geomechanical point of view, unit weight values in the range of 18.6–19.6 kN m⁻³ for silty/sandy layers and 19.8–20.5 kN m⁻³ for the calcarenite layer have been respectively accounted for. A uniaxial compressive strength of about 2.4 MPa has been measured for the Mazzaro material forming the cave roofs (Lollino and Parise, 2010), whereas the tensile strength is about 1∕8–1∕10 of the compressive one, so the parameter m_i of the Hoek–Brown failure criterion is assumed to be equal to m_i=8–10. In the following subsections, the representative conditions of each cavity are shown with respect to the corresponding chart.

3.4.1 Cave A

The stability analysis for cavity A has been carried out with reference to the cross section A-A in Fig. 20. The width and height of the cavity are, respectively, equal to L=7.50 m and h=5.0 m, while the thickness of the resistant portion of the cave roof, which in this case is coincident with the Mazzaro rocky layer, is t=4.30 m. Therefore, the nondimensional ratios are about $L/t\approx \mathrm{1.74}$ and $L/h\approx \mathrm{1.5}$.

With reference to the stratigraphy in Fig. 20, the vertical stress at the depth of the cavity roof is equal to

$$\begin{array}{}\text{(3)}& \begin{array}{rl}{\mathit{\sigma }}_{\mathrm{v}}\approx \left({\mathit{\gamma }}_{\mathrm{1}}\cdot h_{\mathrm{1}}\right)& +\left({\mathit{\gamma }}_{\mathrm{2}}\cdot h_{\mathrm{2}}\right)+\left({\mathit{\gamma }}_{\mathrm{3}}\cdot h_{\mathrm{3}}\right)+\left({\mathit{\gamma }}_{\mathrm{4}}\cdot h_{\mathrm{4}}\right)\\ & +(\mathit{\gamma }\cdot t{)}_{\mathrm{mazzaro}}=\mathrm{324.82}\mathrm{kPa},\end{array}\end{array}$$

so, if ${\mathit{\sigma }}_{\mathrm{c},\min }=\mathrm{2.4}$ MPa, we obtain an operative value of ${\mathit{\sigma }}_{\mathrm{c}}/{\mathit{\sigma }}_{\mathrm{v}}\approx \mathrm{7.39}$.

In Table 5 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Cutrofiano Cave A are shown.

Table 5Geometrical and mechanical parameters and adopted values for stability chart application to the underground Cutrofiano Cave A (Maglio and Ligori, 2014; Parise and Lollino, 2011).

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Figure 22Plan and stratigraphy of the underground cavity C (adapted from Maglio and Ligori, 2014).

3.4.2 Cave B

For cave B the calculation has been performed for section B-B in Fig. 21. It has to be noted that in this case a two-story civil building exists just above the cavity, thus representing a further overburden stress, which has been approximately evaluated equal to q=100 kPa.

The width and the height of the cavity are equal to L=6.80 m and h=5.00 m, respectively, while the thickness of the resistant beam-shaped portion of the roof, i.e., the Mazzaro layer, is t=2.70 m. Therefore, the nondimensional ratios are about $L/t\approx \mathrm{2.52}$ and $L/h\approx \mathrm{1.36}$.

With reference to the stratigraphy in Fig. 21, the vertical stress at the depth of the cavity roof is equal to

$$\begin{array}{}\text{(4)}& \begin{array}{rl}{\mathit{\sigma }}_{\mathrm{v}}\approx \left({\mathit{\gamma }}_{\mathrm{1}}\cdot h_{\mathrm{1}}\right)& +\left({\mathit{\gamma }}_{\mathrm{2}}\cdot h_{\mathrm{2}}\right)+\left({\mathit{\gamma }}_{\mathrm{3}}\cdot h_{\mathrm{3}}\right)+(\mathit{\gamma }\cdot t{)}_{\mathrm{mazzaro}}\\ & +q=\mathrm{277.64}\mathrm{kPa},\end{array}\end{array}$$

so, if σ_c=2.4 MPa, the mobilized value of σ_c∕σ_v is equal to 8.64.

In Table 6 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Cutrofiano Cave B are shown.

Table 6Geometrical and mechanical parameters and adopted values for stability chart application to the underground Cutrofiano Cave B (Maglio and Ligori, 2014; Parise and Lollino, 2011).

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3.4.3 Cave C

For cave C the calculation has been performed for section C-C in Fig. 22. The cave width and height are, respectively, equal to L=5.50 m and h=7.00 m, while the thickness of the resistant roof is t=5.00 m and the corresponding nondimensional ratios result about $L/t\approx \mathrm{1.1}$ and $L/h\approx \mathrm{0.8}$.

In this case, the vertical stress at the depth of the cavity roof is

$$\begin{array}{}\text{(5)}& {\mathit{\sigma }}_{\mathrm{v}}\approx \left({\mathit{\gamma }}_{\mathrm{1}}\cdot h_{\mathrm{1}}\right)+\left({\mathit{\gamma }}_{\mathrm{2}}\cdot h_{\mathrm{2}}\right)+\left({\mathit{\gamma }}_{\mathrm{3}}\cdot h_{\mathrm{3}}\right)+(\mathit{\gamma }\cdot t{)}_{\mathrm{Mazzaro}}=\mathrm{299.7}\mathrm{kPa},\end{array}$$

and, assuming σ_c=2.4 MPa, we obtain ${\mathit{\sigma }}_{\mathrm{c}}/{\mathit{\sigma }}_{\mathrm{v}}\approx \mathrm{8}$.

In Table 7 the geometrical and the mechanical parameters, derived from speleological surveys and material characterization, are reported; moreover, the values adopted for the application of the stability charts to the Cutrofiano Cave C are shown.

Table 7Geometrical and mechanical parameters and adopted values for stability chart application to the underground Cutrofiano Cave C (Maglio and Ligori, 2014; Parise and Lollino, 2011).

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3.4.4 Application of stability chart (m_i=8) to the three underground quarries at Cutrofiano

With calculated values of ratios L∕t and σ_c∕σ_v it is possible, for the three caves A–C of Cutrofiano, to apply a stability chart with a value of m_i=8 as shown in Fig. 23. Based on the L∕h estimated ratios, Cave A and Cave B take into account the light blue curve ($\mathrm{1}\le L/h\le \mathrm{2}$); for Cave C the corresponding curve in the graph is reported in red color ($L/h\le \mathrm{1}$).

Figure 23Application of the stability chart (m_i=8) to the three underground quarries at Cutrofiano.

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It can be pointed out that all the three cavities are in the stable zone of the chart of Fig. 23, although with different safety margins; in fact, the margin of safety for Cave B is low, even for the presence of the overlying building. Cave A and cave C seem to be the most stable, also in relation to the geometry of the caves as well as to the thickness of the Mazzaro resistant layer.